Presents an allegory to illustrate the problem of testing an axiomatic system. A fictitious discussion begins by examining an axiomatic system underlying the intercom system of an association. The discussion continues to examine an unusual model of Euclidean geometry and a model of the noneuclidean geometry discovered by Lobachevsky. (MDH)

An introductory preservice teacher activity from a typical college geometry course is presented. This activity leads the preservice teachers to specific goals, including increased geometric awareness within the everyday environment, appreciation for mathematical modeling techniques, and awareness of methods for teaching geometric concepts to…

This document presents six chapters on four-dimensional geometry, whose titles are: (1) A Brief History; (2) What Is Four-Dimensional Geometry?; (3) Selected Drawings and Models; (4) How to Study the Configurations; (5) Selected Topics; and (6) Applications. The text, suitable for students in advanced levels of secondary school mathematics,…

This guide is support material for geometry teachers in middle schools or high schools in South Carolina. The guide describes the content of each program in the television series and suggests further learning activities for the students. The geometry that underlies the world around us is presented through applications. Contents of the series…